Diagrams.Tangent:$catParam from diagrams-lib-1.3.0.3, E

Percentage Accurate: 99.7% → 99.8%

Time: 2.1s

Alternatives: 4

Speedup: 1.4×

• 75.5% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\left(3 \cdot \left(2 - x \cdot 3\right)\right) \cdot x \]

FPCore

(FPCore (x)
  :precision binary64
  :pre TRUE
  (* (* 3.0 (- 2.0 (* x 3.0))) x))

C

double code(double x) {
	return (3.0 * (2.0 - (x * 3.0))) * x;
}

Fortran

real(8) function code(x)
use fmin_fmax_functions
    real(8), intent (in) :: x
    code = (3.0d0 * (2.0d0 - (x * 3.0d0))) * x
end function

Java

public static double code(double x) {
	return (3.0 * (2.0 - (x * 3.0))) * x;
}

Python

def code(x):
	return (3.0 * (2.0 - (x * 3.0))) * x

Julia

function code(x)
	return Float64(Float64(3.0 * Float64(2.0 - Float64(x * 3.0))) * x)
end

MATLAB

function tmp = code(x)
	tmp = (3.0 * (2.0 - (x * 3.0))) * x;
end

Wolfram

code[x_] := N[(N[(3.0 * N[(2.0 - N[(x * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]

ReFlow

f(x):
	x in [-inf, +inf]
code: THEORY
BEGIN
f(x: real): real =
	((3) * ((2) - (x * (3)))) * x
END code

Initial Program: 99.7% accurate, 1.0× speedup

Math

\[\left(3 \cdot \left(2 - x \cdot 3\right)\right) \cdot x \]

FPCore

(FPCore (x)
  :precision binary64
  :pre TRUE
  (* (* 3.0 (- 2.0 (* x 3.0))) x))

C

double code(double x) {
	return (3.0 * (2.0 - (x * 3.0))) * x;
}

Fortran

real(8) function code(x)
use fmin_fmax_functions
    real(8), intent (in) :: x
    code = (3.0d0 * (2.0d0 - (x * 3.0d0))) * x
end function

Java

public static double code(double x) {
	return (3.0 * (2.0 - (x * 3.0))) * x;
}

Python

def code(x):
	return (3.0 * (2.0 - (x * 3.0))) * x

Julia

function code(x)
	return Float64(Float64(3.0 * Float64(2.0 - Float64(x * 3.0))) * x)
end

MATLAB

function tmp = code(x)
	tmp = (3.0 * (2.0 - (x * 3.0))) * x;
end

Wolfram

code[x_] := N[(N[(3.0 * N[(2.0 - N[(x * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]

ReFlow

f(x):
	x in [-inf, +inf]
code: THEORY
BEGIN
f(x: real): real =
	((3) * ((2) - (x * (3)))) * x
END code

Alternative 1: 99.8% accurate, 1.1× speedup

Math

\[\mathsf{fma}\left(6, x, \left(x \cdot x\right) \cdot -9\right) \]

FPCore

(FPCore (x)
  :precision binary64
  :pre TRUE
  (fma 6.0 x (* (* x x) -9.0)))

C

double code(double x) {
	return fma(6.0, x, ((x * x) * -9.0));
}

Julia

function code(x)
	return fma(6.0, x, Float64(Float64(x * x) * -9.0))
end

Wolfram

code[x_] := N[(6.0 * x + N[(N[(x * x), $MachinePrecision] * -9.0), $MachinePrecision]), $MachinePrecision]

ReFlow

f(x):
	x in [-inf, +inf]
code: THEORY
BEGIN
f(x: real): real =
	((6) * x) + ((x * x) * (-9))
END code

Derivation

1. Initial program 99.7%

   \[\left(3 \cdot \left(2 - x \cdot 3\right)\right) \cdot x \]
2. Step-by-step derivation

3. Applied rewrites 99.8%

   \[\leadsto \mathsf{fma}\left(6, x, \left(x \cdot x\right) \cdot -9\right) \]
4. Add Preprocessing

Alternative 2: 99.8% accurate, 1.4× speedup

Math

\[\mathsf{fma}\left(-9, x, 6\right) \cdot x \]

FPCore

(FPCore (x)
  :precision binary64
  :pre TRUE
  (* (fma -9.0 x 6.0) x))

C

double code(double x) {
	return fma(-9.0, x, 6.0) * x;
}

Julia

function code(x)
	return Float64(fma(-9.0, x, 6.0) * x)
end

Wolfram

code[x_] := N[(N[(-9.0 * x + 6.0), $MachinePrecision] * x), $MachinePrecision]

ReFlow

f(x):
	x in [-inf, +inf]
code: THEORY
BEGIN
f(x: real): real =
	(((-9) * x) + (6)) * x
END code

Derivation

1. Initial program 99.7%

   \[\left(3 \cdot \left(2 - x \cdot 3\right)\right) \cdot x \]
2. Step-by-step derivation

3. Applied rewrites 99.8%

   \[\leadsto \mathsf{fma}\left(-9, x, 6\right) \cdot x \]
4. Add Preprocessing

Alternative 3: 97.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \mathbf{if}\;\left(3 \cdot \left(2 - x \cdot 3\right)\right) \cdot x \leq -2000:\\ \;\;\;\;\left(-9 \cdot x\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;6 \cdot x\\ \end{array} \]

FPCore

(FPCore (x)
  :precision binary64
  :pre TRUE
  (if (<= (* (* 3.0 (- 2.0 (* x 3.0))) x) -2000.0)
  (* (* -9.0 x) x)
  (* 6.0 x)))

C

double code(double x) {
	double tmp;
	if (((3.0 * (2.0 - (x * 3.0))) * x) <= -2000.0) {
		tmp = (-9.0 * x) * x;
	} else {
		tmp = 6.0 * x;
	}
	return tmp;
}

Fortran

real(8) function code(x)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8) :: tmp
    if (((3.0d0 * (2.0d0 - (x * 3.0d0))) * x) <= (-2000.0d0)) then
        tmp = ((-9.0d0) * x) * x
    else
        tmp = 6.0d0 * x
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double tmp;
	if (((3.0 * (2.0 - (x * 3.0))) * x) <= -2000.0) {
		tmp = (-9.0 * x) * x;
	} else {
		tmp = 6.0 * x;
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if ((3.0 * (2.0 - (x * 3.0))) * x) <= -2000.0:
		tmp = (-9.0 * x) * x
	else:
		tmp = 6.0 * x
	return tmp

Julia

function code(x)
	tmp = 0.0
	if (Float64(Float64(3.0 * Float64(2.0 - Float64(x * 3.0))) * x) <= -2000.0)
		tmp = Float64(Float64(-9.0 * x) * x);
	else
		tmp = Float64(6.0 * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = 0.0;
	if (((3.0 * (2.0 - (x * 3.0))) * x) <= -2000.0)
		tmp = (-9.0 * x) * x;
	else
		tmp = 6.0 * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := If[LessEqual[N[(N[(3.0 * N[(2.0 - N[(x * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], -2000.0], N[(N[(-9.0 * x), $MachinePrecision] * x), $MachinePrecision], N[(6.0 * x), $MachinePrecision]]

ReFlow

f(x):
	x in [-inf, +inf]
code: THEORY
BEGIN
f(x: real): real =
	LET tmp = IF ((((3) * ((2) - (x * (3)))) * x) <= (-2000)) THEN (((-9) * x) * x) ELSE ((6) * x) ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 #s(literal 3 binary64) (-.f64 #s(literal 2 binary64) (*.f64 x #s(literal 3 binary64)))) x) < -2e3

   1. Initial program 99.7%

      \[\left(3 \cdot \left(2 - x \cdot 3\right)\right) \cdot x \]

   2. Taylor expanded in x around inf

      \[\leadsto \left(-9 \cdot x\right) \cdot x \]
   3. Step-by-step derivation

   4. Applied rewrites 51.6%

      \[\leadsto \left(-9 \cdot x\right) \cdot x \]

   if -2e3 < (*.f64 (*.f64 #s(literal 3 binary64) (-.f64 #s(literal 2 binary64) (*.f64 x #s(literal 3 binary64)))) x)

   1. Initial program 99.7%

      \[\left(3 \cdot \left(2 - x \cdot 3\right)\right) \cdot x \]

   2. Taylor expanded in x around 0

      \[\leadsto 6 \cdot x \]
   3. Step-by-step derivation

   4. Applied rewrites 51.1%

      \[\leadsto 6 \cdot x \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 4: 51.1% accurate, 3.1× speedup

Math

\[6 \cdot x \]

FPCore

(FPCore (x)
  :precision binary64
  :pre TRUE
  (* 6.0 x))

C

double code(double x) {
	return 6.0 * x;
}

Fortran

real(8) function code(x)
use fmin_fmax_functions
    real(8), intent (in) :: x
    code = 6.0d0 * x
end function

Java

public static double code(double x) {
	return 6.0 * x;
}

Python

def code(x):
	return 6.0 * x

Julia

function code(x)
	return Float64(6.0 * x)
end

MATLAB

function tmp = code(x)
	tmp = 6.0 * x;
end

Wolfram

code[x_] := N[(6.0 * x), $MachinePrecision]

ReFlow

f(x):
	x in [-inf, +inf]
code: THEORY
BEGIN
f(x: real): real =
	(6) * x
END code

Derivation

1. Initial program 99.7%

   \[\left(3 \cdot \left(2 - x \cdot 3\right)\right) \cdot x \]

2. Taylor expanded in x around 0

   \[\leadsto 6 \cdot x \]
3. Step-by-step derivation

4. Applied rewrites 51.1%

   \[\leadsto 6 \cdot x \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2026092 
(FPCore (x)
  :name "Diagrams.Tangent:$catParam from diagrams-lib-1.3.0.3, E"
  :precision binary64
  (* (* 3.0 (- 2.0 (* x 3.0))) x))